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Sebastian Thrun,
Thad Starner,
and
Peter Norvig
Learn about iterative improvement optimization problems and classical algorithms emphasizing gradient-free methods for solving them. These techniques can often be used on intractable problems to find solutions that are "good enough" for practical purposes, and have been used extensively in fields like Operations Research & logistics. Finish the lesson by completing a classroom exercise comparing the different algorithms' performance on a variety of problems.
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What's inside
Syllabus
Thad Starner introduces the concept of _iterative improvement problems_, a class of optimization problems that can be solved with global optimization or local search techniques covered in this lesson.
Read more
Syllabus
Thad Starner introduces the concept of _iterative improvement problems_, a class of optimization problems that can be solved with global optimization or local search techniques covered in this lesson.
Read more
Thad introduces _Hill Climbing_, a very simple local search optimization technique that works well on many iterative improvement problems.
Thad explains _Simulated Annealing_, a classical global optimization technique for optimization.
Thad introduces another optimization technique: _Genetic Algorithms_, which uses a population of samples to make iterative improvements towards the goal.
Complete a classroom exercise implementing simulated annealing to solve the traveling salesman problem.
Review similarities of the techniques introduced in this lesson with links to readings on advanced optimization topics, then complete an optimization exercise in the classroom.
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Develops iterative improvement, hill climbing, simulated annealing, and genetic algorithms skills
Tailored for learners with backgrounds in operations research and logistics
Taught by renowned instructors with expertise in optimization algorithms
Involves hands-on exercises to reinforce learning
Suitable for learners interested in practical problem-solving techniques
Requires prior foundational knowledge in optimization
Save this course
Save (Optional) Optimization Problems to your list so you can find it easily later:
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Activities
Be better prepared
before
your course. Deepen your understanding
during
and
after
it. Supplement your coursework and achieve mastery of the topics covered
in (Optional) Optimization Problems with these
activities:
Review basic probability and statistics concepts
Show steps
Strengthen your foundation in probability and statistics, which are essential for understanding optimization algorithms.
Browse courses on
Probability
Show steps
-
Review notes or textbooks on probability and statistics.
-
Solve practice problems to test your understanding.
Practice basic programming skills
Show steps
Ensure you have a strong foundation in programming before starting the course.
Browse courses on
Programming
Show steps
-
Review basic programming concepts (variables, data types, loops, etc.).
-
Solve simple coding problems to practice your skills.
Read Introduction to Operations Research
Show steps
Reinforce the concepts of optimization and prepare for the course's focus on iterative improvement optimization problems.
View
ISE Introduction to Operations Research
on Amazon
Show steps
-
Review the introduction and first chapter.
-
Summarize the basic concepts of Operations Research.
-
Identify the different types of optimization problems.
-
Solve simple optimization problems using the techniques presented in the book.
Ten other activities
Expand to see all activities and additional details
Show all 13 activities
Review concepts from ‘Introduction to Algorithms’
Show steps
Sharpen your understanding of fundamental algorithms covered in ‘Introduction to Algorithms’. This will provide a solid foundation for the iterative improvement optimization techniques introduced in this course.
Browse courses on
Algorithms
Show steps
-
Revisit key concepts such as time complexity, asymptotic notations and data structures
-
Solve practice problems on algorithm design and analysis
-
Review materials and notes from ‘Introduction to Algorithms’
Follow tutorials on Hill Climbing
Show steps
Gain hands-on experience with one of the core optimization techniques covered in the course.
Show steps
-
Find and follow tutorials on Hill Climbing.
-
Implement Hill Climbing in a programming language of your choice.
-
Apply Hill Climbing to solve simple optimization problems.
Answer questions in the course discussion forum
Show steps
Deepen your understanding of the course material by helping others.
Show steps
-
Participate in the course discussion forum.
-
Answer questions posed by other students.
-
Provide constructive feedback to others' answers.
Implement optimization algorithms in Python
Show steps
Gain hands-on experience implementing the iterative improvement algorithms covered in the course. This will deepen your understanding and build confidence in applying these techniques to real-world optimization problems.
Browse courses on
Python
Show steps
-
Choose an optimization problem from the course materials or online resources
-
Implement the Hill Climbing, Simulated Annealing and Genetic Algorithms algorithms in Python
-
Run the algorithms and compare their performance on the chosen problem
Solve practice problems on Simulated Annealing
Show steps
Strengthen your understanding of Simulated Annealing and its application in solving optimization problems.
Browse courses on
Simulated annealing
Show steps
-
Find and solve practice problems on Simulated Annealing.
-
Analyze the results and evaluate the performance of Simulated Annealing.
Attend a workshop on optimization techniques
Show steps
Expand your knowledge and connect with experts in the field of optimization.
Browse courses on
Optimization Techniques
Show steps
-
Find a workshop on optimization techniques.
-
Attend the workshop and take notes.
-
Network with other attendees and speakers.
Build an optimization tool or application
Show steps
Apply your knowledge to a practical project by building an optimization tool or application. This will provide hands-on experience in designing, developing, and testing optimization solutions.
Browse courses on
Software Development
Show steps
-
Identify a specific optimization problem or domain to focus on
-
Design the architecture and functionality of your tool or application
-
Implement the tool or application using appropriate programming languages and algorithms
-
Test and refine your tool or application to ensure accuracy and efficiency
Build a Genetic Algorithm for solving the Traveling Salesman Problem
Show steps
Apply the concepts of Genetic Algorithms to a real-world optimization problem.
Browse courses on
Genetic algorithms
Show steps
-
Research Genetic Algorithms and their application to the Traveling Salesman Problem.
-
Design and implement a Genetic Algorithm for solving the Traveling Salesman Problem.
-
Evaluate the performance of your Genetic Algorithm on different problem instances.
Document your optimization project
Show steps
Consolidate your learning by documenting the optimization project you worked on. This will help you reflect on your approach, identify areas for improvement, and share your findings with others.
Browse courses on
Technical Writing
Show steps
-
Summarize the problem statement and the optimization algorithms used
-
Describe your implementation and the results you obtained
-
Discuss the challenges faced and lessons learned during the project
Explore advanced optimization techniques
Show steps
Dive deeper into the field of optimization by exploring advanced techniques. This will broaden your knowledge and equip you to tackle more complex optimization problems in the future.
Show steps
-
Identify specific advanced optimization techniques that align with your interests
-
Locate high-quality tutorials or online courses covering these techniques
-
Follow the tutorials, complete exercises, and apply the techniques to practical problems
Review basic probability and statistics concepts
Show steps
Strengthen your foundation in probability and statistics, which are essential for understanding optimization algorithms.
Browse courses on
Probability
Show steps
Show steps
Show steps
- Review notes or textbooks on probability and statistics.
- Solve practice problems to test your understanding.
Practice basic programming skills
Show steps
Ensure you have a strong foundation in programming before starting the course.
Browse courses on
Programming
Show steps
Show steps
Show steps
- Review basic programming concepts (variables, data types, loops, etc.).
- Solve simple coding problems to practice your skills.
Read Introduction to Operations Research
Show steps
Reinforce the concepts of optimization and prepare for the course's focus on iterative improvement optimization problems.
View
ISE Introduction to Operations Research
on Amazon
Show steps
Show steps
Show steps
- Review the introduction and first chapter.
- Summarize the basic concepts of Operations Research.
- Identify the different types of optimization problems.
- Solve simple optimization problems using the techniques presented in the book.
Ten other activities
Expand to see all activities and additional details
Show all 13 activities
Review concepts from ‘Introduction to Algorithms’
Show steps
Sharpen your understanding of fundamental algorithms covered in ‘Introduction to Algorithms’. This will provide a solid foundation for the iterative improvement optimization techniques introduced in this course.
Browse courses on
Algorithms
Show steps
Show steps
Show steps
- Revisit key concepts such as time complexity, asymptotic notations and data structures
- Solve practice problems on algorithm design and analysis
- Review materials and notes from ‘Introduction to Algorithms’
Follow tutorials on Hill Climbing
Show steps
Gain hands-on experience with one of the core optimization techniques covered in the course.
Show steps
Show steps
Show steps
- Find and follow tutorials on Hill Climbing.
- Implement Hill Climbing in a programming language of your choice.
- Apply Hill Climbing to solve simple optimization problems.
Answer questions in the course discussion forum
Show steps
Deepen your understanding of the course material by helping others.
Show steps
Show steps
Show steps
- Participate in the course discussion forum.
- Answer questions posed by other students.
- Provide constructive feedback to others' answers.
Implement optimization algorithms in Python
Show steps
Gain hands-on experience implementing the iterative improvement algorithms covered in the course. This will deepen your understanding and build confidence in applying these techniques to real-world optimization problems.
Browse courses on
Python
Show steps
Show steps
Show steps
- Choose an optimization problem from the course materials or online resources
- Implement the Hill Climbing, Simulated Annealing and Genetic Algorithms algorithms in Python
- Run the algorithms and compare their performance on the chosen problem
Solve practice problems on Simulated Annealing
Show steps
Strengthen your understanding of Simulated Annealing and its application in solving optimization problems.
Browse courses on
Simulated annealing
Show steps
Show steps
Show steps
- Find and solve practice problems on Simulated Annealing.
- Analyze the results and evaluate the performance of Simulated Annealing.
Attend a workshop on optimization techniques
Show steps
Expand your knowledge and connect with experts in the field of optimization.
Browse courses on
Optimization Techniques
Show steps
Show steps
Show steps
- Find a workshop on optimization techniques.
- Attend the workshop and take notes.
- Network with other attendees and speakers.
Build an optimization tool or application
Show steps
Apply your knowledge to a practical project by building an optimization tool or application. This will provide hands-on experience in designing, developing, and testing optimization solutions.
Browse courses on
Software Development
Show steps
Show steps
Show steps
- Identify a specific optimization problem or domain to focus on
- Design the architecture and functionality of your tool or application
- Implement the tool or application using appropriate programming languages and algorithms
- Test and refine your tool or application to ensure accuracy and efficiency
Build a Genetic Algorithm for solving the Traveling Salesman Problem
Show steps
Apply the concepts of Genetic Algorithms to a real-world optimization problem.
Browse courses on
Genetic algorithms
Show steps
Show steps
Show steps
- Research Genetic Algorithms and their application to the Traveling Salesman Problem.
- Design and implement a Genetic Algorithm for solving the Traveling Salesman Problem.
- Evaluate the performance of your Genetic Algorithm on different problem instances.
Document your optimization project
Show steps
Consolidate your learning by documenting the optimization project you worked on. This will help you reflect on your approach, identify areas for improvement, and share your findings with others.
Browse courses on
Technical Writing
Show steps
Show steps
Show steps
- Summarize the problem statement and the optimization algorithms used
- Describe your implementation and the results you obtained
- Discuss the challenges faced and lessons learned during the project
Explore advanced optimization techniques
Show steps
Dive deeper into the field of optimization by exploring advanced techniques. This will broaden your knowledge and equip you to tackle more complex optimization problems in the future.
Show steps
Show steps
Show steps
- Identify specific advanced optimization techniques that align with your interests
- Locate high-quality tutorials or online courses covering these techniques
- Follow the tutorials, complete exercises, and apply the techniques to practical problems
Career center
Learners who complete (Optional) Optimization Problems will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists use data to solve problems and make predictions. They use a variety of techniques, including optimization, to analyze data and build models. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Data Scientists who need to find solutions that are "good enough" for practical purposes.
Operations Research Analyst
Operations Research Analyst
An Operations Research Analyst uses advanced analytical techniques to solve complex problems in a variety of industries, including manufacturing, finance, and healthcare. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Operations Research Analysts who need to find solutions that are "good enough" for practical purposes.
Management Consultant
Management Consultant
Management Consultants help businesses improve their performance. They use a variety of techniques, including optimization, to analyze problems and develop solutions. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Management Consultants who need to find solutions that are "good enough" for practical purposes.
Financial Analyst
Financial Analyst
Financial Analysts use financial data to make investment decisions. They use a variety of techniques, including optimization, to analyze data and build models. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Financial Analysts who need to find solutions that are "good enough" for practical purposes.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems. They use a variety of techniques, including optimization, to improve the performance of their systems. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Software Engineers who need to find solutions that are "good enough" for practical purposes.
Statistician
Statistician
Statisticians use data to understand the world around us. They use a variety of techniques, including optimization, to analyze data and build models. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Statisticians who need to find solutions that are "good enough" for practical purposes.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze financial data. They use a variety of techniques, including optimization, to build models and make predictions. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Quantitative Analysts who need to find solutions that are "good enough" for practical purposes.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess risk and uncertainty. They use a variety of techniques, including optimization, to build models and make predictions. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Actuaries who need to find solutions that are "good enough" for practical purposes.
Business Analyst
Business Analyst
Business Analysts use data to understand business problems and develop solutions. They use a variety of techniques, including optimization, to analyze data and build models. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Business Analysts who need to find solutions that are "good enough" for practical purposes.
Operations Manager
Operations Manager
Operations Managers oversee the day-to-day operations of a business. They use a variety of techniques, including optimization, to improve the efficiency and effectiveness of their operations. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Operations Managers who need to find solutions that are "good enough" for practical purposes.
Transportation Manager
Transportation Manager
Transportation Managers oversee the movement of people and goods. They use a variety of techniques, including optimization, to improve the efficiency and effectiveness of their transportation systems. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Transportation Managers who need to find solutions that are "good enough" for practical purposes.
Supply Chain Manager
Supply Chain Manager
Supply Chain Managers oversee the flow of goods and services from suppliers to customers. They use a variety of techniques, including optimization, to improve the efficiency and effectiveness of their supply chains. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Supply Chain Managers who need to find solutions that are "good enough" for practical purposes.
Logistics Manager
Logistics Manager
Logistics Managers oversee the movement of goods and services from suppliers to customers. They use a variety of techniques, including optimization, to improve the efficiency and effectiveness of their logistics operations. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Logistics Managers who need to find solutions that are "good enough" for practical purposes.
Project Manager
Project Manager
Project Managers plan and execute projects. They use a variety of techniques, including optimization, to manage resources and ensure that projects are completed on time and within budget. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Project Managers who need to find solutions that are "good enough" for practical purposes.
Warehouse Manager
Warehouse Manager
Warehouse Managers oversee the day-to-day operations of a warehouse. They use a variety of techniques, including optimization, to improve the efficiency and effectiveness of their operations. This course provides a strong foundation in optimization techniques, which are essential for success in this role. The course covers a variety of optimization algorithms, including gradient-free methods, which are often used to solve intractable problems. This knowledge will be invaluable to Warehouse Managers who need to find solutions that are "good enough" for practical purposes.
For more career information including salaries, visit:
OpenCourser.com/course/w2yjz8/optional
Reading list
We've selected seven books
that we think will supplement your
learning. Use these to
develop background knowledge, enrich your coursework, and gain a
deeper understanding of the topics covered in
(Optional) Optimization Problems.
Provides intermediate and advanced mathematical optimization. It also provides a good foundation for understanding of optimization techniques.
Provides an intermediate and advanced theory behind optimization using linear algebra techniques to solve optimization problems.
Provides an intermediate and advanced theory behind optimization and provides some good case studies and background for using optimization.
Provides a good foundation for the theory behind convex optimization techniques and provides a good background for understanding some of the limitations behind optimization.
Provides a good selection of optimization problems and case studies.
Provides a wide range of case studies and methods for applied optimization.
Provides a good background for optimization algorithms.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/w2yjz8/optional
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Time
240 hours
Level
Advanced
Via
Udacity
Instructors
Sebastian Thrun
Thad Starner
Peter Norvig
Language
English
Good to know
Develops iterative improvement, hill climbing, simulated annealing, and genetic algorithms skills
Tailored for learners with backgrounds in operations research and logistics
Taught by renowned instructors with expertise in optimization algorithms
Involves hands-on exercises to reinforce learning
Suitable for learners interested in practical problem-solving techniques
Requires prior foundational knowledge in optimization
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